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Created on: 2012-02-04

A sample problem solved by Quickmath web math solver

study techniques to multiply out a sum that comprises 2 terms.

Command

Solve

Equation
X^4-8*X^3+25*X^2+(-34)*X+12 = 0

  1. an equation LHS is equal to a sum comprising 5 terms. The first term of the sum is equal to a power. The base is X. The exponent is four. The second term of the sum is a negative product containing 2 factors. The first factor of the product is equal to eight. The second factor of the product is a power. The base is X. The exponent is three. The third term of the sum is equal to a product that consists of 2 factors. The first factor of the product is equal to twenty five. The second factor of the product is equal to a power. The base is X. The exponent is two. The four term of the sum is equal to a product that comprises 2 factors. The first factor of the product is equal to negative thirty four. The second factor of the product is equal to X. The five term of the sum is equal to twelve RHS is zero.
  2. X to the power of four plus negative eight multiplied by X to the power of three plus twenty five times X to the power of two plus open brace negative thirty four close brace multiplied by X plus twelve is equal to zero.
Variable
Result

Exact

Solution 1 ( complex )
X = -5*(sqrt(3)*%i/2-1/2)/(9*(sqrt(83)/3^(3/2)-46/27)^(1/3))+(sqrt(83)/3^(3/2)-46/27)^(1/3)*(-sqrt(3)*%i/2-1/2)+5/3

  1. an equation Left side of the equation is equal to X RHS is a sum of 3 terms; the first term of the sum is a fraction: the numerator of the fraction is a product that consists of 2 factors; the first factor of the product is negative five; the second factor of the product is equal to a sum that consists of 2 terms; the first term of the sum is equal to a fraction: the top of the fraction is a product that comprises 2 factors; the first factor of the product is equal to square root of three; the second factor of the product is i; the bottom of the fraction is two; the second term of the sum is a negative rational expression: the numerator of the rational expression is one; the denominator of the rational expression is two; the denominator of the fraction is a product containing 2 factors; the first factor of the product is equal to nine; the second factor of the product is a power; the base is a sum that comprises 2 terms; the first term of the sum is equal to a fraction: the numerator of the fraction is square root of eighty three; the denominator of the fraction is a power; the base is three; the exponent is a rational expression: the top of the rational expression is three; the bottom of the rational expression is two; the second term of the sum is a negative fraction: the numerator of the fraction is forty six; the denominator of the fraction is twenty seven; the exponent is a fraction: the top of the fraction is one; the bottom of the fraction is three; the second term of the sum is equal to a product that comprises 2 factors; the first factor of the product is equal to a power; the base is a sum containing 2 terms; the first term of the sum is a rational expression: the top of the rational expression is square root of eighty three; the bottom of the rational expression is a power; the base is three; the exponent is a rational expression: the top of the rational expression is three; the bottom of the rational expression is two; the second term of the sum is equal to a negative fraction: the numerator of the fraction is forty six; the denominator of the fraction is twenty seven; the exponent is a fraction: the top of the fraction is one; the bottom of the fraction is three; the second factor of the product is a sum that comprises 2 terms; the first term of the sum is equal to a fraction: the numerator of the fraction is a product that comprises 2 factors; the first factor of the product is equal to negative square root of three; the second factor of the product is i; the denominator of the fraction is two; the second term of the sum is a negative quotient: dividend of the quotient is one; divisor of the quotient is two; the third term of the sum is equal to a rational expression: the top of the rational expression is five; the bottom of the rational expression is three;
  2. X is negative five times open parenthesis square root of three times i over two plus negative one fraction line two close parenthesis over nine multiplied by left brace square root of eighty three over three exponentiated by three over two plus negative forty six divided by twenty seven right brace raised to the power one fraction line three plus open parenthesis square root of eighty three divided by three raised to the power three divided by two plus negative forty six divided by twenty seven close parenthesis raised to the power of one fraction line three times open parenthesis negative square root of three multiplied by i over two plus negative one fraction line two close parenthesis plus five divided by three.
Solution 2 ( complex )
X = (sqrt(83)/3^(3/2)-46/27)^(1/3)*(sqrt(3)*%i/2-1/2)-5*(-sqrt(3)*%i/2-1/2)/(9*(sqrt(83)/3^(3/2)-46/27)^(1/3))+5/3

  1. an equation LHS is equal to X Right side of the equation is equal to a sum comprising 3 terms. The first term of the sum is a product consisting of 2 factors. The first factor of the product is equal to a power. The base is a sum that contains 2 terms. The first term of the sum is equal to a rational expression: the numerator of the rational expression is square root of eighty three. The denominator of the rational expression is a power. The base is three. The exponent is a quotient: dividend of the quotient is three. Divisor of the quotient is two. The second term of the sum is a negative rational expression: the numerator of the rational expression is forty six. The denominator of the rational expression is twenty seven. The exponent is a quotient: dividend of the quotient is one. Divisor of the quotient is three. The second factor of the product is a sum comprising 2 terms. The first term of the sum is equal to a fraction: the numerator of the fraction is a product that contains 2 factors. The first factor of the product is equal to square root of three. The second factor of the product is equal to i. The denominator of the fraction is two. The second term of the sum is equal to a negative fraction: the numerator of the fraction is one. The denominator of the fraction is two. The second term of the sum is a negative rational expression: the numerator of the rational expression is a product that consists of 2 factors. The first factor of the product is equal to five. The second factor of the product is a sum containing 2 terms. The first term of the sum is a fraction: the top of the fraction is a product that contains 2 factors. The first factor of the product is negative square root of three. The second factor of the product is i. The bottom of the fraction is two. The second term of the sum is a negative fraction: the top of the fraction is one. The bottom of the fraction is two. The denominator of the rational expression is a product of 2 factors. The first factor of the product is equal to nine. The second factor of the product is equal to a power. The base is a sum comprising 2 terms. The first term of the sum is a quotient: dividend of the quotient is square root of eighty three. Divisor of the quotient is a power. The base is three. The exponent is a fraction: the top of the fraction is three. The bottom of the fraction is two. The second term of the sum is equal to a negative quotient: dividend of the quotient is forty six. Divisor of the quotient is twenty seven. The exponent is a fraction: the top of the fraction is one. The bottom of the fraction is three. The third term of the sum is equal to a fraction: the numerator of the fraction is five. The denominator of the fraction is three.
  2. X is equal to open bracket square root of eighty three fraction line three raised to the power three divided by two plus negative forty six over twenty seven close bracket to the power of one fraction line three multiplied by opening parenthesis square root of three multiplied by i over two plus negative one fraction line two closing parenthesis plus negative five times opening parenthesis negative square root of three times i over two plus negative one fraction line two closing parenthesis divided by nine multiplied by left bracket square root of eighty three fraction line three raised to the power three over two plus negative forty six fraction line twenty seven right bracket to the power of one divided by three plus five fraction line three;
Solution 3 ( real )
X = (sqrt(83)/3^(3/2)-46/27)^(1/3)-5/(9*(sqrt(83)/3^(3/2)-46/27)^(1/3))+5/3

  1. an equation LHS is X RHS is equal to a sum that consists of 3 terms; the first term of the sum is equal to a power; the base is a sum that consists of 2 terms; the first term of the sum is equal to a fraction: the top of the fraction is square root of eighty three; the bottom of the fraction is a power; the base is three; the exponent is a rational expression: the numerator of the rational expression is three; the denominator of the rational expression is two; the second term of the sum is equal to a negative fraction: the top of the fraction is forty six; the bottom of the fraction is twenty seven; the exponent is a quotient: dividend of the quotient is one; divisor of the quotient is three; the second term of the sum is equal to a negative fraction: the top of the fraction is five; the bottom of the fraction is a product that consists of 2 factors; the first factor of the product is equal to nine; the second factor of the product is equal to a power; the base is a sum consisting of 2 terms; the first term of the sum is equal to a rational expression: the top of the rational expression is square root of eighty three; the bottom of the rational expression is a power; the base is three; the exponent is a fraction: the top of the fraction is three; the bottom of the fraction is two; the second term of the sum is a negative quotient: dividend of the quotient is forty six; divisor of the quotient is twenty seven; the exponent is a fraction: the top of the fraction is one; the bottom of the fraction is three; the third term of the sum is equal to a rational expression: the numerator of the rational expression is five; the denominator of the rational expression is three;
  2. X is opening brace square root of eighty three over three raised to the power three over two plus negative forty six divided by twenty seven closing brace raised to the power of one over three plus negative five fraction line nine times open brace square root of eighty three fraction line three exponentiated by three fraction line two plus negative forty six over twenty seven close brace exponentiated by one divided by three plus five over three;
Solution 4 ( real )
X = 3

  1. an equation Left side of the equation is equal to X Right side of the equation is three;
  2. X is equal to three;


Approximate

Solution 1 ( complex )
X = 2.23898-1.62767*%i

  1. an equation LHS is X Right side of the equation is equal to a sum containing 2 terms; the first term of the sum is equal to two point two tenth, three hundredth, eight ten hundredth, nine thousandth and eight ten thousandth; the second term of the sum is a negative product of 2 factors; the first factor of the product is equal to one point six tenth, two hundredth, seven ten hundredth, six thousandth and seven ten thousandth; the second factor of the product is equal to i;
  2. X is equal to two point two tenth, three hundredth, eight ten hundredth, nine thousandth and eight ten thousandth plus negative one point six tenth, two hundredth, seven ten hundredth, six thousandth and seven ten thousandth times i.
Solution 2 ( complex )
X = 1.62767*%i+2.23898

  1. an equation Left side of the equation is equal to X Right side of the equation is equal to a sum comprising 2 terms. The first term of the sum is a product that consists of 2 factors. The first factor of the product is one point six tenth, two hundredth, seven ten hundredth, six thousandth and seven ten thousandth. The second factor of the product is i. The second term of the sum is two point two three eight nine eight.
  2. X is equal to one point six tenth, two hundredth, seven ten hundredth, six thousandth and seven ten thousandth multiplied by i plus two point two tenth, three hundredth, eight ten hundredth, nine thousandth and eight ten thousandth;
Solution 3 ( real )
X = .522033

  1. an equation LHS is X Right side of the equation is equal to zero point five tenth, two hundredth, two ten hundredth, three ten thousandth and three hundred thousandth.
  2. X is zero point five tenth, two hundredth, two ten hundredth, three ten thousandth and three hundred thousandth;
Solution 4 ( real )
X = 3.0

  1. an equation Left side of the equation is equal to X RHS is three;
  2. X is equal to three;